Is there any mobile platform that allows me to run Java Applets? In absence of browser integration, at least Java SE capabilities. I've heard of a mobile device capable of running Windows XP - that would probably include support for Java SE and applets; does any one have any hands-on experience with such a device? How well does it perform in terms of Java programs execution?
If you refer to the old school java applets which can be embeded in HTML pages there is IMHO no mobile platform which support this. Applets are written in Java SE, however most platforms I know of have a Java ME runtime.
I don't know how this correlates to the new Java FX as there is a mobile profile coming along with it. Can somebody else comment on this issue?
Given that java applets are traditionally quite simple, yet depend upon the entire JSE stack, including AWT, trying to run an applet on this is not a good choice for mobile java. Unless of coure "mobile" includes tablet pcs. as you say, these run XP and could run the full J2SE stack. This would run your applet unmodified. You can expect a lot of tablets to be released this year to compete with the iPad. E.g. Just one pulled at random. http://www.tabletpc2.com/TEGA_Tablet_to_be_Officially_Launched.html
But if tablets are not what you had in mind, then read on.
If you are starting new development, you will be better served with J2ME, which is far more common on mobile devices. J2ME doesn't support AWT or Swing, but has it's on UI classes. JavaFX is also a candidate, as the mobile profile doesn't depend upon the JSE stack.
If you already have an applet that you want to run on a mobile platform, you may find that porting it is not that difficult. CLDC with MIDP 2.0 has a 2D api (e.g. look at google maps mobile, or opera mobile) and can handle most of the typical tasks appets are used for.
There are certainly a lot of mobile internet devices and netbooks which would allow you to run a java applet. Essentially anything that would run Windows 7/Vista/XP, and many that run linux would allow you to run applets.
As far as how it will perform it probably depend on the applet. I'm sure simple applets will perform just fine. Some applets which do a lot more won't be so fast. Netbooks/MID are as powerful as notebook from maybe 6 or 7 years ago. Java ran just fine on computers from that era, so they should be fine on an MID.